A body is dropped from rest from a tower. It covers 7/16 of the total height during the last second of its motion. Find the total time of fall, in second.
Physics · Kinematics Part-1 (one dimension) · Motion under gravity
JEE Mains NEET

Question

A body is dropped from rest from a tower. It covers 7/16 of the total height during the last second of its motion. Find the total time of fall, in second.

G1 Physics · Accepted Answer

Let total time of fall be T. Total height: H = gT²/2. Distance in the last second: distance in last second = (g/2)[T²−(T−1)²] = (g/2)(2T−1). Given distance in last second/H = 7/16, (2T−1)/T² = 7/16. So 7T² − 32T + 16 = 0. The roots are 4 and 4/7. Since total fall time exceeds 1 s, T=4 s.